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math.AP2018★ 24 cited
Multi-dimensional Burgers equation with unbounded initial data: well-posedness and dispersive estimates
Denis Serre, Luis Silvestre
The Cauchy problem for a scalar conservation laws admits a unique entropy solution when the data is a bounded measurable function (Kruzhkov). The semi-group i…
math.AP2018★ 3 cited
Multi-dimensional scalar conservation laws with unbounded integrable initial data
Denis Serre
We discuss the minimal integrability needed for the initial data, in order that the Cauchy problem for a multi-dimensional conservation law admit an entropy solution. In particular…
math.AP2018
Compensated integrability. Applications to the Vlasov--Poisson equation and other models in mathematical physics
Denis Serre
We extend our analysis of divergence-free positive symmetric tensors (DPT) begun in a previous paper. On the one hand, we refine the statements and give more direct proofs. Next, w…